Development and study of aircraft trajectory control model while flying en-route of four-dimensional area navigation

Dynamics, ballistics, movement control of flying vehicles


Lunev E. M.1*, Neretin E. S.2**, Budkov A. S.2***

1. Integration center branch of the Irkut Corporation, 5, Aviazionny pereulok, Moscow, 125167, Russia
2. ,



This work is devoted to the analysis of the existing algorithms of trajectory control and their updating up to the level of 4-D area navigation (4D-RNAV) for further implementation while developing prospective automatic control systems for en-route flight.

With the advent of satellite systems, navigation has changed qualitatively in the direction of increasing accuracy. However, navigation is only one of the constituent parts of the overall process of flight execution. It should be considered thereupon in general concept, namely, communication, navigation, surveying and organization of the air traffic, developed by ICAO in the 1980-s. The navigation concept of the future developed by ICAO is based on the area navigation.

The area navigation principle allows an aircraft to execute a flight on any desired path and thus realize the advantages of navigation of higher accuracy in improving the structure of air area. It leads to simplifying of air traffic servicing, and foremost decrease of aircraft operating costs.

The planned flight path can be specified not only in the horizontal plane in the form of a route, but also in the vertical plane, by specifying the flight heights of the waypoints, angles or gradients of the trajectory inclination. In addition, a space-time trajectory can be set, when for some points the time of their flyby is specified. In accordance with the dimension of the «space» in which the guidance is carried out, the area navigation is subdivided into three types:

– 2D-RNAV ‒ two-dimensional RNAV in the horizontal plane — LNAV (Lateral Navigation). Sometimes, using a literal translation, it is called lateral navigation, since the guidance is provided only by lateral evasion;

– 3D-RNAV ‒ three-dimensional RNAV in the horizontal and vertical planes. For navigation in the vertical plane, the abbreviation VNAV (Vertical Navigation) is used;

– 4D-RNAV is a four-dimensional RNAV in the horizontal and vertical planes plus the solution of the problem of regulating the speed of flight for passing points of the route or arriving at the aerodrome at a given time. Zone navigation by time is abbreviated as TNAV (Time Navigation). [3]

The problem of area navigation implementation consists not barely in ensuring the flight on an arbitrary path, but in ensuring its accuracy according to the requirement set in the given region. In modern aero Thus, the issues of area navigation were closely interleaved with RNP problems. They were so closely interleaved that these two ranges of issues were incorporated into a single ICAO document «RNP Manual» [1].

Today RNP is considered as a tool for flight technical and regulatory control with RNAV application.

Depending on the strictness of requirements to the accuracy of the specified path following, and the type of functional requirements to onboard equipment the following notations are widely used:

– B-RNAV (Basic RNAV) — the main (basic) area navigation;

– P-RNAV (Precision RNAV) — precise area navigation;

‒ RNP-RNAV — area navigation with required navigation performance.

RNAV is considered by ICAO as the main type of navigation of the future, since it has a number of undeniable advantages over conventional, traditional navigation.


aircraft, Area Navigation (4D-RNAV), trajectory control, modeling, lateral movement stabilization, lengthwise passage control


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